To jointly evaluate VaR and ES forecasts associated to each stock market index, in addition to the results of the coverage tests, Table REF  reports the values of the loss functions \(S_{FZN}\)  of [1]} and \(S_{FZ0}\)  of [2]}, averaged over the out-of-sample period where:
\(S_{FZN}({\cal Q}_{t}, ES_t, y_t) = (\mathbf {1}_{(y_t < {\cal Q}_{t})} - \tau ) \frac{{\cal Q}_{t}}{2 \tau \sqrt{- ES_t}} - \frac{1}{2 \sqrt{- ES_t}} (\mathbf {1}_{(y_t < {\cal Q}_{t})} \frac{y_t}{\tau } - ES_t) + \sqrt{- ES_t}\) 
